[Resource Topic] 2013/731: Constructing Differentially 4-uniform Permutations over GF(2^{2k}) from the Inverse Function Revisited

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Title:
Constructing Differentially 4-uniform Permutations over GF(2^{2k}) from the Inverse Function Revisited

Authors: Yongqiang Li, Mingsheng Wang, Yuyin Yu

Abstract:

Constructing S-boxes with low differential uniformity and high nonlinearity is of cardinal significance in cryptography. In the present paper, we show that numerous differentially 4-uniform permutations over GF(2^{2k}) can be constructed by composing the inverse function and cycles over GF(2^{2k}). Two sufficient conditions are given, which ensure that the differential uniformity of the corresponding compositions equals 4. A lower bound on nonlinearity is also given for permutations constructed with the method in the present paper. Moreover, up to CCZ-equivalence, a new differentially 4-uniform permutation with the best known nonlinearity over GF(2^{2k}) with k odd is constructed. For some special cycles, necessary and sufficient conditions are given such that the corresponding compositions are differentially 4-uniform.

ePrint: https://eprint.iacr.org/2013/731

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